In known short inking units of the foregoing type, the applicator rolls have a diameter which corresponds to the diameter of the form cylinder. Although what are referred to as ghost images are avoided on the printing material as a result of the uniformity of diameters, applicator rolls that are the same size as the form cylinder require a large amount of space which is usually very scarce in printing presses. For this reason, known short inking units usually comprise only one applicator roll. It is not possible in that case to use a plurality of applicator rolls due to the space constraints. Because of the large diameter of the applicator roll, there also is a large amount of ink in the inking unit of such known arrangements. As a consequence, it takes a relatively long time until a constant ink/dampening solution emulsion is attained. Moreover, since there is only one applicator roll there is a very low number of nip points, which also makes it difficult to form a constant ink/dampening solution emulsion. A further disadvantage of the known arrangements is that changing the format is made difficult because the diameter of the applicator rolls is tied to the diameter of the form cylinder. Furthermore, applicator rolls of the same size as the form cylinder require very hard roll coverings which are expensive.